0.40g of an organic compound containing 40.67% carbon and 8.47% hydrogen gave in dumas method 75.92 ml nitrogen gas at NTP. what is empirical formula of the compound.

To determine the empirical formula of the organic compound, we need to analyze the given data step by step. The Dumas method allows us to find the nitrogen content in the compound, which is essential for our calculations. Let's break this down into manageable parts.

Step 1: Calculate the Moles of Nitrogen

First, we need to find out how many moles of nitrogen gas (N₂) were produced. At Normal Temperature and Pressure (NTP), 1 mole of any gas occupies 22.4 liters (or 22,400 mL). Given that 75.92 mL of nitrogen gas was produced, we can calculate the moles of nitrogen:

• Volume of nitrogen gas = 75.92 mL
• Moles of nitrogen = Volume (mL) / 22,400 mL/mol

Calculating this gives:

Moles of nitrogen = 75.92 mL / 22,400 mL/mol = 0.00339 moles of N₂

Step 2: Determine the Amount of Nitrogen in the Compound

Since nitrogen gas (N₂) consists of two nitrogen atoms, we need to find the moles of nitrogen atoms:

• Moles of nitrogen atoms = 2 × Moles of N₂

This results in:

Moles of nitrogen atoms = 2 × 0.00339 = 0.00678 moles of N

Step 3: Calculate the Masses of Carbon and Hydrogen

Next, we can find the masses of carbon and hydrogen in the compound using the percentages provided:

• Mass of carbon = 40.67% of 0.40 g = 0.40 g × 0.4067 = 0.16268 g
• Mass of hydrogen = 8.47% of 0.40 g = 0.40 g × 0.0847 = 0.03388 g

Step 4: Calculate the Moles of Carbon and Hydrogen

Now, we convert these masses into moles:

• Moles of carbon (C) = Mass of carbon / Molar mass of carbon (12 g/mol)
• Moles of hydrogen (H) = Mass of hydrogen / Molar mass of hydrogen (1 g/mol)

Calculating these gives:

Moles of carbon = 0.16268 g / 12 g/mol = 0.01356 moles of C

Moles of hydrogen = 0.03388 g / 1 g/mol = 0.03388 moles of H

Step 5: Determine the Ratio of Moles

Now, we have the moles of each element:

• C: 0.01356
• H: 0.03388
• N: 0.00678

To find the simplest whole number ratio, we divide each by the smallest number of moles, which is 0.00678:

• Ratio of C = 0.01356 / 0.00678 = 2.00
• Ratio of H = 0.03388 / 0.00678 = 5.00
• Ratio of N = 0.00678 / 0.00678 = 1.00

Step 6: Write the Empirical Formula

From these ratios, we can express the empirical formula as:

C₂H₅N

Thus, the empirical formula of the organic compound is C₂H₅N. This formula represents the simplest whole number ratio of the elements present in the compound, providing a foundational understanding of its composition.